Ground-state scattering lengths for potassium isotopes determined by double-resonance photoassociative spectroscopy of ultracold39K

Abstract

We use double-resonance photoassociative spectroscopy of ultracold ${}^{39}\mathrm{K}$ atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free ${}^{39}\mathrm{K}$ atoms to the pure long-range ${0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=2)$ level is followed by stimulated emission to high-lying levels of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potential. The binding energies of levels within 5 GHz below the lowest ground-state ${4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)$ hyperfine asymptote are measured by both trap loss and ionization detection. The locations of these near-threshold hyperfine-coupled molecular levels allow us to constrain the triplet potential and thereby determine the triplet scattering length. The result for ${}^{39}\mathrm{K},$ ${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$ ${(1a}_{0}=0.0529177 \mathrm{nm}),$ is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large ${}^{39}\mathrm{K}$ Bose-Einstein condensate will not be stable.